10th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2009

General Instructions:
1. All questions are compulsory.
2. The question paper consists of 30 questions divided into four
sections - A, B, C and D. Section A comprises
of ten questions of 1 mark each, Section B comprises of five
questions of 2marks each, Section C comprises of ten questions of 3
marks each and Section D comprises of five questions of 6marks
each.
3. All questions in Section A are to be answered in one word, one
sentence or as per the exact requirement of the question.
There is no overall choice. However, an internal choice has been
provided in one question of 2 marks each, three questions of 3
marks each and two questions of 6 marks each. You have to attempt
only one of the alternatives in all such questions.
4. In question on construction, the drawing should be neat and as
per the given measurements.
5. Use of calculators is not permitted.

Q1 :

Find the [HCF × LCM] for the numbers 100 and 190.

Answer :

For two numbers a and b, HCF
× LCM = a × b

∴ For the given numbers 100 and 190:

HCF × LCM = 100 × 190

HCF × LCM = 19000

Q2 :

If 1 is a zero of the polynomial p(x) = ax2 −
3(a − 1) x − 1, then
find the value of a.

Answer :

If 1 is a zero of polynomial p(x), then p(1) = 0.

∴ p(1) = a(1)2 − 3(a − 1) (1) − 1 =
0

⇒ a − 3a + 3 − 1
= 0

⇒ −2a = −2

⇒ a = 1

Thus, the value of a is 1.

Q3 :

In ΔLMN, ∠L = 50° and ∠N = 60°. If
ΔLMN ∼ ΔPQR, then find ∠Q.

Answer :

∠L + ∠M + ∠N = 180° (Angle sum property)

Substituting ∠L = 50° and ∠N = 60° in this
equation:

50° + ∠M + 60° = 180°

∠M = 70°

It is given that ΔLMN ∼ ΔPQR.

We know that corresponding angles in similar triangles are of
equal measures.

The area of an equilateral triangle is cm2. Taking each
angular point as centre, circles are drawn with radius equal to
half the length of the side of the triangle. Find the area of
triangle not included in the circles. [Take= 1.73]

OR

Figure 5 shows a decorative block which is made of
two solids − a cube and a hemisphere. The base of the block
is a cube with edge 5 cm and the hemisphere, fixed on the top,
has a diameter of 4.2 cm. Find the total surface area of the
block. [Takeπ=]

An aeroplane when flying at a height of 3125 m from the ground
passes vertically below another plane at an instant when the
angles of elevation of the two planes from the same point on the
ground are 30° and 60° respectively. Find the distance
between the two planes at that instant.

A juice seller serves his customers using a glass
as shown in Figure 6. The innerdiameter of
the cylindrical glass is 5 cm, but the bottom of the glass has a
hemispherical portion raised which reduces the capacity of the
glass. If the height of the glass is 10 cm, find the apparent
capacity of the glass and its actual capacity. (Useπ= 3.14)

OR

A cylindrical vessel with internal diameter 10 cm and height 10.5
cm is full of water. A solid cone of base diameter 7 cm and
height 6 cm is completely immersed in water. Find the volume of